Noether's Theorem as a Metaphor for Chargaff's 2nd Parity Rule in Genomics.

In the present note, the genomic compositional rule largely known as 'Chargaff's 2nd parity rule' (asserting equimolarity between Adenine-Thymine and Guanine-Cytosine in any of the two DNA strands) is regarded in association with Noether's theorem linking symmetries with conservation laws in physics. In the case of the genome, the strict physical and mathematical prerequisites of Noether's theorem do not hold. However, we conclude that a metaphor can be established with Noether's theorem, as inter-strand symmetry concerning DNA functionality engenders specific features in genome composition. Inversely, when inter-strand symmetry does not hold, the corresponding quantitative relations fail to appear. This association is also considered from the point of view of the existence of emergent laws and properties in evolutionary genomics.

A decision support system for the identification of metastases of Metastatic Melanoma using whole-body FDG PET/CT images.

Metastatic Melanoma (MM) is an aggressive type of cancer which produces metastases throughout the body with very poor survival rates. Recent advances in immunotherapy have shown promising results for controlling disease's progression. Due to the often rapid progression, fast and accurate diagnosis and treatment response assessment is vital for the whole patient management. These procedures prerequisite accurate, whole-body tumor identification. This can be offered by the imaging modality Positron Emission Tomography (PET)/Computed Tomography (CT) with the radiotracer F 18-Fluorodeoxyglucose (FDG). However, manual segmentation of PET/CT images is a very time-consuming and labor intensive procedure that requires expert knowledge. Most of the previously published segmentation techniques focus on a specific type of tumor or part of the body and require a great amount of manually labeled data, which is, however, difficult for MM. Multimodal analysis of PET/CT is also crucial because FDG-PET contains only the functional information of tumors which can be complemented by the anatomical information of CT. In this paper, we propose a whole-body segmentation framework capable of efficiently identifying the highly heterogeneous tumor lesions of MM from the whole-body 3D FDG-PET/CT images. The proposed decision support system begins with an Ensemble Unsupervised Segmentation of regions of high FDG-uptake based on Fuzzy C-means and a custom region growing algorithm. Then, a region classification model based on radiomics features and Neural Networks classifies these regions as tumors or not. Experimental results showed high performance in the identification of MM lesions with Sensitivity 83.68%, Specificity 91.82%, F1-score 75.42%, AUC 94.16% and Balanced accuracy 87.75% which were also supported by the public dataset evaluation.

Fractal and Multifractal Analysis of PET-CT Images for Therapy Assessment of Metastatic Melanoma Patients under PD-1 Inhibitors: A Feasibility Study.

Longitudinal whole-body PET-CT scans with F-18-fluorodeoxyglucose (18F-FDG) in patients suffering from metastatic melanoma were analyzed and the tracer distribution in patients was compared with that of healthy controls. Nineteen patients with metastatic melanoma were scanned before, after two and after four cycles of treatment with PD-1 inhibitors (pembrolizumab, nivolumab) applied as monotherapy or as combination treatment with ipilimumab. For comparison eight healthy controls were analyzed. As quantitative measures for the comparison between controls and patients, the nonlinear fractal dimension (FD) and multifractal spectrum (MFS) were calculated from the digitized PET-CT scans. The FD and MFS measures, which capture the dispersion of the tracer in the body, decreased with disease progression, since the tracer particles tended to accumulate around metastatic sites in patients, while the measures increased when the patients' clinical condition ameliorate. The MFS measure gave better predictions and were consistent with the PET Response Evaluation Criteria for Immunotherapy (PERCIMT) in 81% of the cases, while FD agreed in 77% of all cases. These results agree, qualitatively, with a previous study of our group when treatment with ipilimumab monotherapy was considered.

Finite Size Effects in Networks of Coupled Neurons.

We use extensive computer simulations to study synchronization phenomena in networks of biological neurons. Each individual neuron is modeled using the leaky integrate-and-fire (LIF) scheme, while many neurons are coupled nonlocally in a network. In this system chimera states develop, which are complex states consisting of coexisting synchronous and asynchronous network areas. We study the influence of the network size on the properties and the form of chimera states. We show that for constant coupling strength, the number of the synchronous/asynchronous domains depends quantitatively on the coupling ratio. This dependence allows to extract synchronization properties in large ensembles of neurons after extrapolating from simulations of small networks. Since computer simulations of even small neuron networks are highly demanding in memory and CPU time, this property is particularly important in view of the large number of neurons involved in any cognitive function. In total, the number of neurons in the human brain is of the order of 1010, and each of them is connected with an average of 103 other neurons.

Quantifying local randomness in human DNA and RNA sequences using Erdös motifs.

In 1932, Paul Erdös asked whether a random walk constructed from a binary sequence can achieve the lowest possible deviation (lowest discrepancy), for the sequence itself and for all its subsequences formed by homogeneous arithmetic progressions. Although avoiding low discrepancy is impossible for infinite sequences, as recently proven by Terence Tao, attempts were made to construct such sequences with finite lengths. We recognize that such constructed sequences (we call these "Erdös sequences") exhibit certain hallmarks of randomness at the local level: they show roughly equal frequencies of short subsequences, and at the same time exclude trivial periodic patterns. For the human DNA we examine the frequency of a set of Erdös motifs of length-10 using three nucleotides-to-binary mappings. The particular length-10 Erdös sequence is derived from the length-11 Mathias sequence and is identical with the first 10 digits of the Thue-Morse sequence, underscoring the fact that both are deficient in periodicities. Our calculations indicate that: (1) the purine(A and G)/pyridimine(C and T) based Erdös motifs are greatly underrepresented in the human genome, (2) the strong(G and C)/weak(A and T) based Erdös motifs are slightly overrepresented, (3) the densities of the two are negatively correlated, (4) the Erdös motifs based on all three mappings being combined are slightly underrepresented, and (5) the strong/weak based Erdös motifs are greatly overrepresented in the human messenger RNA sequences.

Erratum: Chimera patterns in two-dimensional networks of coupled neurons [Phys. Rev. E 95, 032224 (2017)].

This corrects the article DOI: 10.1103/PhysRevE.95.032224.

Chimera patterns in two-dimensional networks of coupled neurons.

We discuss synchronization patterns in networks of FitzHugh-Nagumo and leaky integrate-and-fire oscillators coupled in a two-dimensional toroidal geometry. A common feature between the two models is the presence of fast and slow dynamics, a typical characteristic of neurons. Earlier studies have demonstrated that both models when coupled nonlocally in one-dimensional ring networks produce chimera states for a large range of parameter values. In this study, we give evidence of a plethora of two-dimensional chimera patterns of various shapes, including spots, rings, stripes, and grids, observed in both models, as well as additional patterns found mainly in the FitzHugh-Nagumo system. Both systems exhibit multistability: For the same parameter values, different initial conditions give rise to different dynamical states. Transitions occur between various patterns when the parameters (coupling range, coupling strength, refractory period, and coupling phase) are varied. Many patterns observed in the two models follow similar rules. For example, the diameter of the rings grows linearly with the coupling radius.

Fractal and multifractal analysis of PET/CT images of metastatic melanoma before and after treatment with ipilimumab.

BACKGROUND: PET/CT with F-18-fluorodeoxyglucose (FDG) images of patients suffering from metastatic melanoma have been analysed using fractal and multifractal analysis to assess the impact of monoclonal antibody ipilimumab treatment with respect to therapy outcome. RESULTS: Thirty-one cases of patients suffering from metastatic melanoma have been scanned before and after two and after four cycles of treatment. For each patient, we calculated the fractal and multifractal dimensions using the box-counting method on the digitalised PET/CT images of all three studies to assess the therapeutic outcome. We modelled the spreading of malignant cells in the body via kinetic Monte Carlo simulations to address the dynamical evolution of the metastatic process and to predict the spatial distribution of malignant lesions. Our analysis shows that the fractal dimensions which describe the tracer dispersion in the body decrease consistently with the deterioration of the patient's therapeutic outcome condition. In 20 out of 24 cases, the fractal analysis results match those of the treatment outcome as defined by the oncologists, while 7 cases are considered as special cases because the patients had non-tumour-related findings or side effects which affect the results. The decrease in the fractal dimensions with the deterioration of the patient conditions (in terms of disease progression) is attributed to the hierarchical localisation of the tracer which accumulates in the affected lesions and does not spread homogeneously throughout the body. Fractality emerges as a result of the migration patterns which the malignant cells follow for propagating within the body (circulatory system, lymphatic system). Analysis of the multifractal spectrum complements and supports the results of the fractal analysis. In the kinetic Monte Carlo modelling of the metastatic process, a small number of malignant cells diffuse through a fractal medium representing the blood circulatory network. Along their way, the malignant cells engender random metastases (colonies) with a small probability and, as a result, fractal spatial distributions of the metastases are formed similar to the ones observed in the PET/CT images. CONCLUSIONS: The Monte Carlo-generated spatial distribution of metastases changes with time approaching values close to the ones recorded in the metastatic patients. Thus, we propose that fractal and multifractal analyses have potential applications in quantification of the evaluation of PET/CT images to monitor the disease evolution as well as the response to different medical treatments. The proposed approach, being operator independent, can offer new diagnostic tools in parallel to the visual location of the lesions and may improve multiparameter assessment of FDG PET/CT studies.

Controlling chimera states: The influence of excitable units.

We explore the influence of a block of excitable units on the existence and behavior of chimera states in a nonlocally coupled ring-network of FitzHugh-Nagumo elements. The FitzHugh-Nagumo system, a paradigmatic model in many fields from neuroscience to chemical pattern formation and nonlinear electronics, exhibits oscillatory or excitable behavior depending on the values of its parameters. Until now, chimera states have been studied in networks of coupled oscillatory FitzHugh-Nagumo elements. In the present work, we find that introducing a block of excitable units into the network may lead to several interesting effects. It allows for controlling the position of a chimera state as well as for generating a chimera state directly from the synchronous state.

Chimera states in population dynamics: Networks with fragmented and hierarchical connectivities.

We study numerically the development of chimera states in networks of nonlocally coupled oscillators whose limit cycles emerge from a Hopf bifurcation. This dynamical system is inspired from population dynamics and consists of three interacting species in cyclic reactions. The complexity of the dynamics arises from the presence of a limit cycle and four fixed points. When the bifurcation parameter increases away from the Hopf bifurcation the trajectory approaches the heteroclinic invariant manifolds of the fixed points producing spikes, followed by long resting periods. We observe chimera states in this spiking regime as a coexistence of coherence (synchronization) and incoherence (desynchronization) in a one-dimensional ring with nonlocal coupling and demonstrate that their multiplicity depends on both the system and the coupling parameters. We also show that hierarchical (fractal) coupling topologies induce traveling multichimera states. The speed of motion of the coherent and incoherent parts along the ring is computed through the Fourier spectra of the corresponding dynamics.

Robustness of chimera states for coupled FitzHugh-Nagumo oscillators.

Chimera states are complex spatio-temporal patterns that consist of coexisting domains of spatially coherent and incoherent dynamics. This counterintuitive phenomenon was first observed in systems of identical oscillators with symmetric coupling topology. Can one overcome these limitations? To address this question, we discuss the robustness of chimera states in networks of FitzHugh-Nagumo oscillators. Considering networks of inhomogeneous elements with regular coupling topology, and networks of identical elements with irregular coupling topologies, we demonstrate that chimera states are robust with respect to these perturbations and analyze their properties as the inhomogeneities increase. We find that modifications of coupling topologies cause qualitative changes of chimera states: additional random links induce a shift of the stability regions in the system parameter plane, gaps in the connectivity matrix result in a change of the multiplicity of incoherent regions of the chimera state, and hierarchical geometry in the connectivity matrix induces nested coherent and incoherent regions.

Evolutionary constraints favor a biophysical model explaining hox gene collinearity.

The Hox gene collinearity enigma has often been approached using models based on biomolecular mechanisms. The biophysical model is an alternative approach based on the hypothesis that collinearity is caused by physical forces pulling the Hox genes from a territory where they are inactive to a distinct spatial domain where they are activated in a step by step manner. Such Hox gene translocations have recently been observed in support of the biophysical model. Genetic engineering experiments, performed on embryonic mice, gave rise to several unexpected mutant expressions that the biomolecular models cannot predict. On the contrary, the biophysical model offers convincing explanation. Evolutionary constraints consolidate the Hox clusters and as a result, denser and well organized clusters may create more efficient physical forces and a more emphatic manifestation of gene collinearity. This is demonstrated by stochastic modeling with white noise perturbing the expression of Hox genes. As study cases the genomes of mouse and amphioxus are used. The results support the working hypothesis that vertebrates have adopted their comparably more compact Hox clustering as a tool needed to develop more complex body structures. Several experiments are proposed in order to test further the physical forces hypothesis.

Coupled intermittent maps modeling the statistics of genomic sequences: A network approach.

The dynamics of coupled intermittent maps is used to model the correlated structure of genomic sequences. The use of intermittent maps, as opposed to other simple chaotic maps, is particularly suited for the production of long-range correlation features which are observed in the genomic sequences of higher eucaryotes. A weighted network approach to symbolic sequences is introduced, and it is shown that coupled intermittent polynomial maps produce degree and link size distributions with power-law exponents similar to the ones observed in real genomes. The proposed network approach to symbolic sequences is generic and can be applied to any symbol sequence (artificial or natural).

Alu and LINE1 distributions in the human chromosomes: evidence of global genomic organization expressed in the form of power laws.

Spatial distribution and clustering of repetitive elements are extensively studied during the last years, as well as their colocalization with other genomic components. Here we investigate the large-scale features of Alu and LINE1 spatial arrangement in the human genome by studying the size distribution of interrepeat distances. In most cases, we have found power-law size distributions extending in several orders of magnitude. We have also studied the correlations of the extent of the power law (linear region in double-logarithmic scale) and of the corresponding exponent (slope) with other genomic properties. A model has been formulated to explain the formation of the observed power laws. According to the model, 2 kinds of events occur repetitively in evolutionary time: random insertion of several types of intruding sequences and occasional loss of repeats belonging to the initial population due to "elimination" events. This simple mechanism is shown to reproduce the observed power-law size distributions and is compatible with our present knowledge on the dynamics of repeat proliferation in the genome.

Local sequential minimization of double stranded B-DNA using Monte Carlo annealing.

A software algorithm has been developed to investigate the folding process in B-DNA structures in vacuum under a simple and accurate force field. This algorithm models linear double stranded B-DNA sequences based on a local, sequential minimization procedure. The original B-DNA structures were modeled using initial nucleotide structures taken from the Brookhaven database. The models contain information at the atomic level allowing one to investigate as accurately as possible the structure and characteristics of the resulting DNA structures. A variety of DNA sequences and sizes were investigated containing coding and non-coding, random and real, homogeneous or heterogeneous sequences in the range of 2 to 40 base pairs. The force field contains terms such as angle bend, Lennard-Jones, electrostatic interactions and hydrogen bonding which are set up using the Dreiding II force field and defined to account for the helical parameters such as twist, tilt and rise. A close comparison was made between this local minimization algorithm and a global one (previously published) in order to find out advantages and disadvantages of the different methods. From the comparison, this algorithm gives better and faster results than the previous method, allowing one to minimize larger DNA segments. DNA segments with a length of 40 bases need approximately 4 h, while 2.5 weeks are needed with the previous method. After each minimization the angles between phosphate-oxygen-carbon A1, the oxygen-phosphate-oxygen A2 and the average helical twists were calculated. From the generated fragments it was found that the bond angles are A1=150 degrees +/-2 degrees and A2=130 degrees +/-10 degrees, while the helical twist is 36.6 degrees +/-2 degrees in the A strand and A1=150 degrees +/-6 degrees and A2=130+/-6 degrees with helical twist 39.6 degrees +/-2 degrees in the B strand for the DNA segment with the same sequence as the Dickerson dodecamer.

Complexity and non-linear description of diurnal cortisol and growth hormone secretory patterns before and after sleep deprivation.

OBJECTIVE: The circadian secretory profiles of cortisol and growth hormone (hGH) in normal subjects are interrelated. Slight alterations in cortisol secretion are paralleled by similar ones of hGH secretion. Under physiological conditions an inhibitory effect of glucocorticoids on hGH secretion is more potent than a stimulatory one, while in normal young subjects the nychtohemeral cortisol and hGH levels are lower and higher, respectively, post 24 hours total sleep-deprivation, compared to baseline values. The aim of the present work was to further assess the qualitative characteristics of the 24-hour secretory patterns of these two hormones before and after 24 hours total sleep deprivation, by studying their non-linear profiles using fractal analysis. METHODS: Cortisol and hGH were measured in 24-hour samples drawn from 10 healthy men (mean age SD: 24 +/- 1 yr, mean BMI SD: 25 +/- 1 kg/m2) before and after 24 hours total sleep deprivation. Twenty-four hour blood sampling was performed serially every 30 min the day before and the day after total sleep deprivation. The 24-hour hormone profiles were analyzed by Fourier spectrum, in order to verify periodicities; the corresponding attractors were drawn and their respective fractal dimensions were calculated using the box counting method. RESULTS: Diurnal cortisol levels before sleep deprivation gave rise to a fractal attractor with a D0 fractal dimension of 2.65 +/- 0.03, which decreased, post-sleep deprivation, to D0: 2.18 +/- 0.04. Growth hormone before sleep deprivation gave rise to a fractal attractor with a D0 dimension of 1.96 +/- 0.60, which increased to 2.24 +/- 0.60 post-sleep deprivation. These post-sleep deprivation changes of the fractal dimensions of cortisol and hGH, suggest that sleep deprivation leads to a more regular secretory profile of cortisol, while it tends to render hGH secretory profile less regular. Additionally, these changes of the fractal dimensions parallell the previously described quantitative overall changes of these hormones. CONCLUSIONS: The post-sleep deprivation decrease of cortisol fluctuation might reflect the mechanism by which sleep deprivation temporarily improves mood in melancholic depression, a condition associated with hyperactivity of the hypothalamic-pituitary-adrenal axis.